What is the justification for each step in solving the inequality? −2(x+1)≥3x+8 select from the drop-down menus to correctly justify each step. −2(x+1)≥3x+8 given −2x−2≥3x+8 −2x≥3x+10 −5x≥10 x≤−2

Hi Anna,

Question:

What is the justification for each step in solving the inequality?

−2(x+1)≥3x+8

Select from the drop-down menus to correctly justify each step.

Solution:

−2x − 2 ≥ 3x + 8

Subtract 3x from both sides.

−2x − 2 − 3x ≥ 3x + 8 − 3x

−5x − 2 ≥ 8

Add 2 to both sides.

−5x − 2 + 2 ≥ 8 + 2

−5x ≥ 10

Divide both sides by -5

x = -2

The only step she needs to fix is option C instead of being −2x ≥ 3x + 10 it should be  −2x − 2 − 3x ≥ 3x + 8 − 3x  then −5x − 2 + 2 ≥ 8 + 2 then divide both sides by 5. She needs to add those three steps.

The volume of the roof rounded to the nearest tenths is 2226.56 ft³

Step-by-step explanation:

We note that the shape of the cross section of the roof is that of a triangle, whereby the volume in this case is the product of the length of the roof and the area of the triangular cross section as follows;

Area of the roof triangular cross section =

Width of the roof, W = 14.25 ft

Height of the roof, h = 2.5 ft

∴ Roof cross sectional area =

Length of roof = 125 ft

Hence, volume of root = Roof cross sectional area × Roof length

∴ Volume of root = 17.8125 ft² × 125 ft = 2226.56 ft³

The volume of the roof rounded to the nearest tenths = 2226.56 ft³.